12,086 research outputs found
On the Achievable Rates of Decentralized Equalization in Massive MU-MIMO Systems
Massive multi-user (MU) multiple-input multiple-output (MIMO) promises
significant gains in spectral efficiency compared to traditional, small-scale
MIMO technology. Linear equalization algorithms, such as zero forcing (ZF) or
minimum mean-square error (MMSE)-based methods, typically rely on centralized
processing at the base station (BS), which results in (i) excessively high
interconnect and chip input/output data rates, and (ii) high computational
complexity. In this paper, we investigate the achievable rates of decentralized
equalization that mitigates both of these issues. We consider two distinct BS
architectures that partition the antenna array into clusters, each associated
with independent radio-frequency chains and signal processing hardware, and the
results of each cluster are fused in a feedforward network. For both
architectures, we consider ZF, MMSE, and a novel, non-linear equalization
algorithm that builds upon approximate message passing (AMP), and we
theoretically analyze the achievable rates of these methods. Our results
demonstrate that decentralized equalization with our AMP-based methods incurs
no or only a negligible loss in terms of achievable rates compared to that of
centralized solutions.Comment: Will be presented at the 2017 IEEE International Symposium on
Information Theor
Hearing the clusters in a graph: A distributed algorithm
We propose a novel distributed algorithm to cluster graphs. The algorithm
recovers the solution obtained from spectral clustering without the need for
expensive eigenvalue/vector computations. We prove that, by propagating waves
through the graph, a local fast Fourier transform yields the local component of
every eigenvector of the Laplacian matrix, thus providing clustering
information. For large graphs, the proposed algorithm is orders of magnitude
faster than random walk based approaches. We prove the equivalence of the
proposed algorithm to spectral clustering and derive convergence rates. We
demonstrate the benefit of using this decentralized clustering algorithm for
community detection in social graphs, accelerating distributed estimation in
sensor networks and efficient computation of distributed multi-agent search
strategies
Gossip Dual Averaging for Decentralized Optimization of Pairwise Functions
In decentralized networks (of sensors, connected objects, etc.), there is an
important need for efficient algorithms to optimize a global cost function, for
instance to learn a global model from the local data collected by each
computing unit. In this paper, we address the problem of decentralized
minimization of pairwise functions of the data points, where these points are
distributed over the nodes of a graph defining the communication topology of
the network. This general problem finds applications in ranking, distance
metric learning and graph inference, among others. We propose new gossip
algorithms based on dual averaging which aims at solving such problems both in
synchronous and asynchronous settings. The proposed framework is flexible
enough to deal with constrained and regularized variants of the optimization
problem. Our theoretical analysis reveals that the proposed algorithms preserve
the convergence rate of centralized dual averaging up to an additive bias term.
We present numerical simulations on Area Under the ROC Curve (AUC) maximization
and metric learning problems which illustrate the practical interest of our
approach
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling
The goal of decentralized optimization over a network is to optimize a global
objective formed by a sum of local (possibly nonsmooth) convex functions using
only local computation and communication. It arises in various application
domains, including distributed tracking and localization, multi-agent
co-ordination, estimation in sensor networks, and large-scale optimization in
machine learning. We develop and analyze distributed algorithms based on dual
averaging of subgradients, and we provide sharp bounds on their convergence
rates as a function of the network size and topology. Our method of analysis
allows for a clear separation between the convergence of the optimization
algorithm itself and the effects of communication constraints arising from the
network structure. In particular, we show that the number of iterations
required by our algorithm scales inversely in the spectral gap of the network.
The sharpness of this prediction is confirmed both by theoretical lower bounds
and simulations for various networks. Our approach includes both the cases of
deterministic optimization and communication, as well as problems with
stochastic optimization and/or communication.Comment: 40 pages, 4 figure
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